Do Muggles also live in places such as Godric's Hollows, Hogsmeade and Diagon Alley as well as other towns and villages with magical populations? If yes, do they refer to those places using different names to the wizarding world?
I don't think that Muggles live in places like Hogsmeade or Diagon Alley because they are well protected not to be recognized from Muggles. But they could live in Godric's Hollow cause its just a "normal" village, just filled up with a lot of witches and wizards!
In the first book when Harry and Hagrid arrive in London and stand in front of the Leaky Cauldron, Harry mentions that it seems that only Hagrid and him can see the entrance to the pub and the Muggles just look over it as if it wasn't there. And since the entrance to Diagon Alley is in the back of the Leaky Cauldron, Muggles can't have knowledge of Diagon Alley.
Or just think about Hogwarts and how it is protected from Muggles: If Muggles come near, they just see an old ruin with a sign not to enter it because the roof could come down any minute. And if they still wanna go in, the Anti-Muggle-Spell comes into action and the Muggles feel a sudden urge to leave.
So Hogwarts and Godric's Hollow could be known by the Muggles (Hogwarts as old ruin), but Hogsmeade and Diagon Alley are too well protected to be known or to be habit to some muggles.
There are two parts to this answer:
In general, Muggles and magical folk seem to share towns/cities.
There are a few exceptions.
Obviously, Diagon Alley, the Leaky Cauldron and the underlying streets are entirely hidden from Muggle eyes, as they’d instantly give away the existence of magic.
And we’re told that Hogsheade is magic-only:
“Do you know much about Hogsmeade?” asked Hermione keenly. “I’ve read it’s the only entirely non-Muggle settlement in Britain —”
— Prisoner of Azkaban, chapter 5 (The Dementor)
Of course, this probably isn’t quite accurate. There are probably small hamlets and rural areas where you can only find magical folk, but which are considered insignificant. But it implies that all large settlements are a mixture of Muggles and magic.
That would include Godric’s Hollow (and indeed, the Potters’s memorial mentions Muggles), and presumably other large towns and cities.
It seems likely that they use the same names.
When Hermione’s reading about Godric’s Hollow, we learn that wizards went into hiding in 1689. Prior to that, we know (from Pottermore, among other places) that wizards and Muggles mingled together. It seems likely that before the Statute of Secrecy, they used the same names for towns/cities as Muggles, and there’s nothing to suggest they tried to choose different names after the Statute was signed.
Since place names change at a very slow place, it seems likely that they’re still using the same names for most places as Muggles. Here’s the relevant passage:
“Upon the signature of the International Statute of Secrecy in 1689, wizards went into hiding for good. It was natural, perhaps, that they formed their own small communities within a community. Many small villages and hamlets attracted several magical families, who banded together for mutual support and protection. The villages of Tinworth in Cornwall, Upper Flagley in Yorkshire, and Ottery St. Catchpole on the south coast of England were notable homes to knots of Wizarding families who lived alongside tolerant and sometimes Confunded Muggles. Most celebrated of these half-magical dwelling places is, perhaps, Godric’s Hollow.”
— Deathly Hallows, chapter 16 (Godric’s Hollow)
(The three villages mentioned in that text are entirely fictional. That may imply that there is a large collection of magical-only villages, but too small to be compared to Hogsmeade.)